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We review how the AdS2 × S2, AdS3 × S3 and AdS5 × S5 superstring theories in the Pohlmeyer-reduced form exhibit hidden [Formula: see text], [Formula: see text] and [Formula: see text] worldsheet supersymmetries, with emphasis on the last two cases. Their characteristic feature is the presence of non-local terms in the supersymmetry transformations.

In this paper, we present the proof of a no-ghost theorem for the bosonic string in Nappi–Witten spacetime by the BRST-technology. The key point in this proof is to compare the characters with the signature functions, where traces are taken over the whole state space. It includes the states of Nappi–Witten string, the states of some extra unitary CFT and the conformal ghost states. Only the signature function of the Nappi–Witten string part is not trivial. Here we obtain it in a new complete basis for the states space of Nappi–Witten string. For all real number b, which is a parameter of the Nappi–Witten metric, the characters and the signature functions are exactly equivalent. Then we can state that the physical string states in Nappi–Witten group are all of non-negative norm.

Compactifications of the heterotic string are a viable route to phenomenologically realistic vacua and interesting new mathematics. While supergravity aspects of heterotic compactifications are largely well-understood their worldsheet description remains largely unexplored. We review recent work in developing linear sigma model techniques aimed at elucidating the underlying worldsheet description.

In this paper, the singularities of the geometry for four classes of worldsheets, which are respectively, located in three-dimensional hyperbolic space and three-dimensional de Sitter space–time are considered. Under the theoretical frame of geometry of space–time and as applications of singularity theory, it is shown that these worldsheets have two classes of singularities, that is, in the local sense, these four classes of worldsheets are, respectively, diffeomorphic to the cuspidal edge and the swallowtail. The first hyperbolic worldsheet and the second hyperbolic worldsheet are [Formula: see text]-dual to the tangent curves of spacelike curves. Moreover, it is also revealed that there is a close relationship between the types of singularities of worldsheets and a geometric invariant [Formula: see text], depending on whether [Formula: see text] or [Formula: see text] and [Formula: see text], the singularities of these worldsheets can be characterized by the geometric invariant. We provide two explicit examples of worldsheets to illustrate the theoretical results.

We construct a sequence of nilpotent BRST charges in RNS superstring theory, based on new gauge symmetries on the worldsheet, found in this paper. These new local gauge symmetries originate from the global nonlinear space-time $\alpha$-symmetries, shown to form a noncommutative ground ring in this work. The important subalgebra of these symmetries is $U(3)\times{X_6}$, where $X_6$ is solvable Lie algebra consisting of 6 elements with commutators reminiscent of the Virasoro type. We argue that the new BRST charges found in this work describe the kinetic terms in string field theories around curved backgrounds of the $AdS\times{CP}_n$-type, determined by the geometries of hidden extra dimensions induced by the global $\alpha$-generators. The identification of these backgrounds is however left for the work in progress., Comment: 31 pages, typos corrected

The issue of space time gauge invariance for the bosonic string has been earlier addressed using the loop variable formalism. In this paper the question of obtaining a gauge invariant action for the open bosonic string is discussed. The derivative w.r.t $ln a$ (where $a$ is a world sheet cutoff) of the partition function - which is first normalized by dividing by the integral of the two point function of a marginal operator - is a candidate for the action. Applied to the zero-momentum tachyon it gives a tachyon potential that is similar to those that have been obtained using Witten's background independent formalism. This procedure is easily made gauge invariant in the loop variable formalism by replacing $ln a$ by $\Sigma$ which is the generalization of the Liouville mode that occurs in this formalism. We also describe a method of resumming the Taylor expansion that is done in the loop variable formalism. This allows one to see the pole structure of string amplitudes that would not be visible in the original loop variable formalism., Comment: 19 pages, Latex file

We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on non-covariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit non-covariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wider applicability to covariant theories that are not Weyl invariant, but where covariant tensor operators are desired. After constructing covariantly regularized vertex operators, we define a class of background-independent path integral measures suitable for string quantization. We show how gauge invariance of the path integral implies the usual physical state conditions in a very conceptually clean way. We then discuss the construction of the BRST action from first principles, obtaining some interesting caveats relating to its general covariance. In our approach, the expected BRST related anomalies are encoded somewhat differently from other approaches. We conclude with an unusual but amusing derivation of the value $D= 26$ of the critical dimension., Comment: 64 pages, minor edits in exposition

In this paper we study the phenomenon of UV/IR mixing in noncommutative field theories from the point of view of world-sheet open-closed duality in string theory. New infrared divergences in noncommutative field theories arise as a result of integrating over high momentum modes in the loops. These are believed to come from integrating out additional bulk closed string modes. We analyse this issue in detail for the bosonic theory and further for the supersymmetric theory on the $C^2/Z_2$ orbifold. We elucidate on the exact role played by the constant background $B$-field in this correspondence., Comment: 65 pages, 11 figures, invited article for IJMPA, references added

We study a Ramond–Neveu–Schwarz string with one end fixed on a D0-brane and the other end free as a qualitative guide to the spectrum of hadrons containing one very heavy quark. The mixed boundary conditions break half of the worldsheet supersymmetry and allow only odd α and even d modes in the Ramond sector, while the Neveu–Schwarz oscillators b's become odd-integer moded. Boson-fermion masses can still be matched if space–time is nine-dimensional; thus SO(8) triality still plays a role in the spectrum, although full space–time supersymmetry does not survive. We quantize the system in a temporal-like gauge where X0 ~ τ. Although the gauge choice eliminates negative-norm states at the outset, there are still even-moded Virasoro and even (odd) moded super-Virasoro constraints to be imposed in the NS(R) sectors. The Casimir energy is now positive in both sectors; there are no tachyons. States for α′ M2 ≤ 13/4 are explicitly constructed and found to be organized into SO(8) irreps by (super)constraints, which include a novel "[Formula: see text]" operator in the Neveu–Schwarz and Γ0 ± I in the Ramond sectors. GSO projections are not allowed. The preconstraint states above the ground state have matching multiplicities, indicating space–time supersymmetry is broken by the (super)constraints. A distinctive physical signature of the system is a slope twice that of the open RNS string. When both ends are fixed, all leading and subleading trajectories are eliminated, resulting in a spectrum qualitatively similar to the J/ψ and ϒ particles.

We construct a Neveu-Schwarz-Ramond superstring model which is invariant under supersymmetric U(1)_V * U(1)_A gauge transformations as well as the super-general coordinate, the super local Lorentz and the super-Weyl transformations on the string world-sheet. We quantize the superstring model by covariant BRST formulation a la Batalin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantizations the model turns out to be formulated consistently in 10+2-dimensional background spacetime involving two time dimensions., Comment: 1+61 pages, no figures, LaTeX

The tremendous progress achieved through the study of black holes and branes suggests that their time dependent generalizations called Spacelike branes (S-branes) may prove similarly useful. An example of an established approach to S-branes is to include a string boundary interaction and we first summarize evidence for the death of open string degrees of freedom for the homogeneous rolling tachyon on a decaying brane. Then, we review how to extract the flat S-brane worldvolumes describing the homogeneous rolling tachyon and how large deformations correspond to creation of lower dimensional strings and branes. These S-brane worldvolumes are governed by S-brane actions which are on equal footing to D-brane actions, since they are derived by imposing conformality on the string worldsheet, as well as by analyzing fluctuations of time dependent tachyon configurations. As further examples we generalize previous solutions of the S-brane actions so as to describe multiple decaying and nucleating closed fundamental strings. Conceptually S-brane actions are therefore different from D-brane actions and can provide a description of time dependent strings/branes and possibly their interactions., Comment: 15 pages, 7 eps figures; invited review for Modern Physics Letters A, including new solutions for S-brane actions. v2 published version, minor typos corrected

A string in four dimensions is constructed by supplementing it with 44 Majorana fermions. The later are represented by 11 vectors in the bosonic representation SO (D-1,1). The central charge is 26. The fermions are grouped in such a way that the resulting action is worldsheet supersymmetric. The energy–momentum and current generators satisfy the super-Virasoro algebra. GSO projections are necessary for proving modular invariance. Space–time supersymmetry algebra is deduced and is substantiated for specific modes of zero mass. The symmetry group of the model can descend to the low energy standard model group SU (3)× SU L(2)× U Y(1) through the Pati–Salam group.

In this paper some properties of the superstring with noncommutative worldsheet are studied. We study the noncommutativity of the spacetime, generalization of the Poincar\'e symmetry of the superstring, the changes of the metric, antisymmetric tensor and dilaton., Comment: 11 pages, Latex, no figure, a new action and some references have been added

Conformal field theory of the D1/D5 system and superstrings on AdS3 × S3 × T4 is studied with particular attention to the worldsheet fields corresponding to the T4 part. A solution to the space–time N = 4 superconformal symmetry doubling and other problems is proposed. It is argued that the relevant space–time symmetry should be based on the middle N = 4 superconformal algebra. It is discussed as to why this superconformal structure has been missed so far.

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein-like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for space–time gravity, even in the absence of other matter fields.

We attempt to construct new superstring actions with a $D$-plet of Majorana fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time index and $A$ is the two dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the world-sheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some non-locality because of bilinear terms of $\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action with $\psi^{\cal B}_A$ is difficult are finally discussed., Comment: 12 pages, Latex, both title and abstract are changed, discussion of some relations among our results, Nambu-Goto string and super Yang-Mills theories, added. Results unchanged

Making use of the duality transformation, we derive in the Londons' limit of the Abelian Higgs model string representation for the 't Hooft loop average defined on the string worldsheet, which yields the values of two coefficient functions parametrizing the bilocal correlator of the dual field strength tensors. The asymptotic behaviors of these functions agree with the ones obtained within the method of vacuum correlators in QCD in the lowest order of perturbation theory. We demonstrate that the bilocal approximation to the method of vacuum correlators is an exact result in the Londons' limit, i.e. all the higher cumulants in this limit vanish. We also show that at large distances, apart from the integration over metrics, the obtained string effective theory (which in this case reduces to the nonlinear massive axionic sigma model) coincides with the low energy limit of the dual version of 4D compact QED, the so-called universal confining string theory. We derive string tension of the Nambu–Goto term and the coupling constant of the rigidity term for the obtained string effective theory and demonstrate that the latter is always negative, which means the stability of strings, while the positiveness of the former is confirmed by the present lattice data. These data enable us to find the Higgs boson charge and the vacuum expectation value of the Higgs field, which well-described QCD. We also study dynamics of the weight factor of the obtained string representation for the 't Hooft average in the loop space. In conclusion, we obtain string representation for the partition function of the correlators of an arbitrary number of Higgs currents, by virtue of which we rederive the structure of the bilocal correlator of the dual field strength tensors, which yields the surface term in the string effective action.

We construct a locally supersymmetric action for the scalar particle, and study its relation with the usual reparametrization invariant action. The mechanisms at work are similar to those employed in the embedding of the bosonic string into the fermionic one, originally due to Berkovits and Vafa in their search for a universal string. The simpler algebraic structure present in the particle case provides us with a guide on how to prove in a simple way, without the need of fixing the superconformal gauge, that the supersymmetric formulation of the bosonic string is equivalent to the usual one, where reparametrization invariance is the only world-sheet gauge symmetry., Comment: 8 pages, REVTEX

We summarize recent work, in which we consider scattering amplitudes of non-critical strings in the limit where the energy of all external states is large compared to the string tension. We show that the high energy limit is dominated by a saddle point that can be mapped onto an electrostatic equilibrium configuration of an assembly of charges associated with the external states, together with a density of charges arising from the Liouville field. The Liouville charges accumulate on line segments, which produce quadratic branch cuts on the worldsheet. The electrostatics problem is solved for string tree level in terms of hyperelliptic integrals and is given explicitly for the 3- and 4-point functions. For generic values of the central charge, the high energy limit behaves in a string-like fashion, with exponential energy dependence., Comment: 10pp, LaTeX, Contribution to Proceedings of the Telluride 1996, workshop on Low-Dimensional Quantum Fields Theory

We examine the change induced in the worldsheet geometry of a relativistic membrane under a conformal rescaling of the spacetime metric. As the induced transformation of the intrinsic geometry is obvious, the extrinsic geometry can be transformed nontrivially. By identifying the worldsheet scalars which transform multiplicatively, we can construct actions for extended objects which are conformally invariant.

Superstring models on Weyl orbifolds are investigated in [Formula: see text] heterotic string theories. Some of the Weyl orbifold models are shown to be consistent with worldsheet supersymmetry, N=1 spacetime supersymmetry and modular invariance. Two ways of embedding in [Formula: see text] are studied and residual gauge groups are classified.

The three loop ladder diagram is a graph with six links and four cubic vertices that contributes to the D^{12} R^4 amplitude at genus one in type II string theory. The vertices represent the insertion points of vertex operators on the toroidal worldsheet and the links represent scalar Green functions connecting them. By using the properties of the Green function and manipulating the various expressions, we obtain a modular invariant Poisson equation satisfied by this diagram, with source terms involving one, two and three loop diagrams. Unlike the source terms in the Poisson equations for diagrams at lower orders in the momentum expansion or the Mercedes diagram, a particular source term involves a five point function containing a holomorphic and a antiholomorphic worldsheet derivative acting on different Green functions. We also obtain simple equalities between topologically distinct diagrams, and consider some elementary examples., Comment: 23 pages, LaTeX, 29 figures

We introduce a new type of the spacetime quantization based on the spinorial description suggested by loop quantum gravity. Specifically, we build our theory on a string theory inspired $Spin(3,1)$ worldsheet action. Because of its connection with quantum gravity theories, our proposal may in principle link back to string theory, connect to loop quantum gravity where $SU(2)$ is suggested as the fundamental symmetry, or serve as a Lorentzian spin network. We derive the generalized uncertainty principle and demonstrate the holographic nature of our theory. Due to the quantization of spacetime, geodesics in our theory are fuzzy, but the fuzziness is shown to be much below conceivable astrophysical bounds., Comment: Accepted for publication by IJMPD, 6 pages. arXiv admin note: text overlap with arXiv:1512.03157

We describe a scenario for inflation in the framework of non-critical string theory, which does not employ an inflaton field. There is an exponential expansion of the volume of the Universe, induced by enormous entropy production in the early stages of cosmological evolution. This is associated with the loss of information carried by global string modes that cross the particle horizon. It is the same loss of information that induces irreversible time flow when target time is identified with the world-sheet Liouville mode. The resulting scenario for inflation is described by a string analogue of the Fokker-Planck equation that incorporates diffusion and dissipative effects. Cosmological density perturbations are naturally small., Comment: 17 pages LATEX

We will show how the refined holomorphic anomaly equation obeyed by the Nekrasov partition function at generic [Formula: see text], [Formula: see text] values becomes compatible, in a certain two-parameter expansion, with the assumption that both parameters are associated to genus counting. The underlying worldsheet theory will be analyzed and constrained in various ways, and we will provide both physical interpretation and some alternative evidence for this model. Finally, we will use the Gopakumar–Vafa formulation for the refined topological string in order to give a more quantitative description.

We study the energy loss rate (ELR) of the accelerated quark in terms of the holographic models for the two different motions, linear acceleration and uniform rotation. They are examined by two different non-conformal models with confinement. We found in both models that the value of ELR is bounded from below by the string tension of the linear confinement potential between quark and anti-quark. The lower bounds of ELR are independent of the types of the motion of the quark. They are determined by the string tension at the world sheet horizon of the model. These results are obtained when the model has the diagonal background metric., 10 pages, 4 figures

As an example of our noncritical string approach to microscopic black hole dynamics, we exhibit some string contributions to the [Formula: see text] matrix relating in- and out-state density matrices that do not factorize as a product of S and S† matrices. They are associated with valley trajectories between topological defects on the string worldsheet, that appear as quantum fluctuations in the space-time foam. Through their uv renormalization scale dependences these valleys cause non-Hamiltonian time evolution and suppress off-diagonal entries in the density matrix at large times. Our approach is a realization of previous formulations of nonequilibrium quantum statistical mechanics with an arrow of time.

It is known that Nambu–Goto extended objects present some pathological structures, such as cusps and kinks, during their evolution. In this paper, we propose a model through the generalized Raychaudhuri (Rh) equation for membranes to determine if there are cusps and kinks in the worldsheet. We extend the generalized Rh equation for membranes to allow the study of the effect of higher order curvature terms in the action on the issue of cusps and kinks, using it as a tool for determining when a Nambu–Goto string generates cusps or kinks in its evolution. Furthermore, we present three examples where we test graphically this approach.

Exact and explicit string solutions propagating in 2+1 dimensional de Sitter spacetime are presented and physically analized. (In this case the string equations reduce to a sinh-Gordon model.) Strings generically tend to inflate or either to collapse. The world-sheet time τ interpolates between the cosmic (τ→±∞) and conformal (τ→0) times. For τ→0, the typical string instability is found, while for τ→±∞, a new string behavior appears. In that regime, the string expands (or contracts) but not with the same rate as the universe does. The string constraints select periodic solutions of the sinh-Gordon equation associated to the lower boundary of the allowed zone, therefore excluding elliptic solutions.

T-Duality invariant worldsheet string actions, recently written down by Schwarz and Sen, are coupled to the worldsheet gauge fields. It is shown that the integration of the dual coordinates gives the conventional, vector, axial and chiral, gauged string actions for the appropriate choice of the gauged isometries. Alternatively, the gauge field integration is shown to give a T-duality invariant action which matches with the corresponding results known earlier., Comment: (minor mixup in notations have been corrected), 15 pages, IP/BBSR/93-32

We have made a modification of a very heuristic relationship available in the literature between the parameter space distance and the embedding space distance on the string worldsheet. This modification along with the input of numerically determined values of the fractal dimension of the fermionic worldsheet and of the Wilson scaling dimensions of conventional ψ2 and ψ4-field theories enables a numerical calculation of the critical exponents α and β of the 3D Ising model. These values are in very good agreement with the experimental and other theoretical values.

We present a geometric interpretation for the torsion constraints in (2,0) supergravity using G-structures. This leads to a classification of the constraints as given by Ref. 1. We also present the essential torsion constraints for (p,q) geometry.

We study the properties of amplitudes in the closed string theory based on the N=2 worldsheet supergravity. The one-loop correction to the three-point amplitude is computed and compared to the effective field theory result. We discuss the peculiar kinematics arising from the (2, 2) signature of the space-time and its role in the factorization properties of the amplitudes.

We consider strings with an N=2 local superconformal symmetry on the worldsheet. The critical dimension for this theory is four (two complex dimensions) with the signature (2, 2). A Kähler function giving rise to self-dual gravity is the only physical degree of freedom of this theory. Some miraculous symmetries are observed corresponding to the exchange of worldsheet and target moduli. The open and heterotic versions of this string theory correspond to self-dual Yang-Mills fields coupled to self-dual gravity in four dimensions.

Sine-square deformation, a recently found modulation of the coupling strength in certain statistical models, is discussed in the context of two-dimensional conformal field theories, with particular attention to open/closed string duality. This deformation is shown to be non-trivial and leads to a divergence in the worldsheet metric. The structure of the vacua of the deformed theory is also investigated. The approach advocated here may provide an understanding of string duality through the worldsheet dynamics., Comment: 15 pages, 4 figures

All the models of elementary particles and their interactions derived from String Theory involve a compact six-dimensional internal space. Its volume and shape should be fixed or stabilized, since otherwise massless scalar fields (moduli) reflecting their deformations appear in our four-dimensional space-time, with sizable effects on known particles and fields. We propose a strategy towards stabilizing the compact space without fluxes of three-form fields from closed strings. Our main motivation and goal is to proceed insofar as possible within conventional string world-sheet theory. As we shall see, D-branes with magnetic flux ("magnetized D-branes") and the forces between them can be used to this end. We investigate here some necessary ingredients: open string one-loop vacuum amplitudes between magnetized D-branes, magnetized D-branes fixed at orbifold singularities, and potential energies among such D-branes in the compact space that result from tree-level closed string exchanges., Comment: 23 pages, 2 figures

The question "What lies beyond the Quantized String or Superstring Theory?" and the question "What lies beyond Quantum Mechanics itself?" might have one common answer: a discretized, classical version of string theory, which lives on a lattice in Minkowski space. The size a of the meshes on this lattice in Minkowski space is determined by the string slope parameter, α′.

We show performing general "0-brane reduction" along an arbitrary fixed direction in spacetime and applied to the starting point of minimal, off-shell 4D, $\cal N$ $=$ 1 irreducible supermultiplets, yields adinkras whose adjacency matrices are among some of the special cases proposed by Kuznetsova, Rojas, and Toppan. However, these more general reductions also can lead to `Garden Algebra' structures beyond those described in their work. It is also shown that for light-like directions, reduction to the 0-brane breaks the equality in the number of fermions and bosons for dynamical theories. This implies that light-like reductions should be done instead to the space of 1-branes or equivalently to the worldsheet., 17 pages, corrected reference, added note at the end, various typo corrections

We consider circular spinning string solutions in AdS5×T1, 1 and calculate the quantum corrections to the energy at one-loop on worldsheet. The fluctuations are given as a set of harmonic oscillators and we calculate their normal mode frequency in closed form. The sum of frequency is equal to the one-loop string energy, which through AdS/CFT correspondence corresponds to the leading order correction of the conformal dimension for long operators in Klebanov–Witten conifold gauge field theory.

It is shown that the bosonic non-linear sigma model with torsion may be reinterpreted as a non-linear sigma model formulated on an algebraically extended two-dimensional worldsheet. The torsion term arises naturally as a consequence of the extended geometry. The two models, while locally equivalent, have distinct global features.